Theory of photoluminescence of the ν=1 quantum Hall state:Excitons, spin waves, and spin textures

We study the theory of intrinsic photoluminescence of two-dimensional electron systems in the vicinity of the ν=1 quantum Hall state. We focus predominantly on the recombination of a band of initial ``excitonic states'' that are the low-lying energy states of our model at ν=1. It is shown that the recombination of excitonic states can account for recent observations of the polarization-resolved spectra of a high-mobility GaAs quantum well. The asymmetric broadening of the spectral line in the ${\mathrm{\sigma }}_{\mathrm{-}}$ polarization is explained to be the result of the ``shakeup'' of spin waves upon radiative recombination of excitonic states. We derive line shapes for the recombination of excitonic states in the presence of long-range disorder that compare favorably with the experimental observations. We also discuss the stabilities and recombination spectra of other (``charged'') initial states of our model. An additional high-energy line observed in experiment is shown to be consistent with the recombination of a positively charged state. The recombination spectrum of a negatively charged initial state, predicted by our model but not observed in the present experiments, is shown to provide a direct measure of the formation energy of the smallest ``charged spin texture'' of the ν=1 state.